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Gradient potential estimates in elliptic obstacle problems with Orlicz growth

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Abstract

In this paper,we consider the solutions of the non-homogeneous elliptic obstacle problems with Orlicz growth involving measure data. We first establish the pointwise estimates of the approximable solutions to these problems via fractional maximal operators. Furthermore, we obtain pointwise and oscillation estimates for the gradients of solutions by the non-linear Wolff potentials, and these yield results on \(C^{1,\alpha }\)-regularity of solutions.

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Acknowledgements

The authors are supported by the National Natural Science Foundation of China (NNSF Grant No. 12071229 and No. 12101452) and the Tianjin postgraduate research and innovation project (Grant No. 2021YJSB016). The authors would like to express their gratitude to the anonymous reviewers for their constructive comments and suggestions that improved the last version of the manuscript.

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Authors and Affiliations

  1. School of Mathematical Sciences, Nankai University, Tianjin, 300071, China

    Qi Xiong

  2. School of Mathematical Sciences and LPMC, Nankai University, Tianjin, 300071, China

    Zhenqiu Zhang

  3. School of Mathematical Sciences, Tianjin Normal University, Tianjin, 300387, China

    Lingwei Ma

Authors
  1. Qi Xiong
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  2. Zhenqiu Zhang
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  3. Lingwei Ma
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Correspondence to Zhenqiu Zhang.

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Communicated by A. Mondino.

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Xiong, Q., Zhang, Z. & Ma, L. Gradient potential estimates in elliptic obstacle problems with Orlicz growth. Calc. Var. 61, 83 (2022). https://doi.org/10.1007/s00526-022-02196-6

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